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Interacting one-dimensional fermionic symmetry-protected topological phases.

Evelyn Tang1, Xiao-Gang Wen

  • 1Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.

Physical Review Letters
|September 26, 2012
PubMed
Summary
This summary is machine-generated.

Interactions can change topological phases in one-dimensional superconductors. All four symmetry-protected topological phases, even with strong interactions, are achievable with free fermions.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Materials
  • Topological Phases

Background:

  • Topological phases in free fermion systems are classified by Abelian groups (0, Z2, Z).
  • One-dimensional fermionic superconductors with spin-rotation (Sz) and time-reversal symmetries are typically classified by Z.
  • Understanding the impact of interactions on these classifications is crucial for materials science.

Purpose of the Study:

  • To investigate how weak and strong interactions modify the topological classification of one-dimensional fermionic superconductors.
  • To determine if strongly interacting topological phases can be realized in noninteracting (free fermion) systems.
  • To generalize the classification for different discrete symmetries.

Main Methods:

  • Group cohomology theory was employed to analyze topological phases.
  • Projective representations were compared to identify distinct phases.
  • The study focused on one-dimensional fermionic superconducting systems with specific symmetries.

Main Results:

  • Weak interactions reduce the classification of one-dimensional superconductors from Z to Z4.
  • Even with strong interactions, only four distinct symmetry-protected topological phases exist.
  • All four identified phases can be realized using free fermions.
  • The classification depends on the order of discrete Z(n) symmetries: Z4 for even n and Z2 for odd n.

Conclusions:

  • Interactions significantly alter topological phase classifications in one-dimensional superconductors.
  • The rich physics of strongly interacting topological phases can be effectively mimicked by simpler free fermion systems.
  • The developed approach is applicable to other symmetry classes and dimensions for topological phase discovery.